Gould-Hsu反演和Hagen-Rothe型卷积

Gould-Hsu inversions and Hagen-Rothe type convolutions

通过引入分母因式,定义了四种Hagen-Rothe型卷积.它们本身没有封闭的表达式.通过逆序和线性组合,Andrews和Burge的两个恒等式产生了另外的四个卷积公式.以这四个公式为出发点,利用Gould-Hsu反演,建立了四对与Hagen-Rothe型卷积相关的对称公式.

Four kinds of Hagen-Rothe type convolutions were defined by introducing denominator factors. They have no closed expressions themselves. Two identities due to Andrews and Burge produced other four convolution formulas by means of reversals and linear combinations. Starting from these four formulae and using Gould-Hsu inversions, four pairs of reciprocal formulas with respect to Hagen-Rothe type convolutions were established.